and both share a common ground at "ID":
If you have a ground fault at or near "ID" that could be the cause of your fuse failure, and could be related to the shift lock malfunction. IIRC, ground point "ID" is at the lower left corner of the dash support panel (the removable sheet metal panel...
This is a problem you really need the EWD to solve. Here's the shift lock circuit:
The shift lock solenoid is connected to the stop light switch, and then to the stop light fuse. It is not directly connected to the headlight circuit. FWIW, the "E" terminal at the lower right is a ground.